Argumentation theory has become an important topic in the field of AI. The basic idea is to construct arguments in favor and against a statement, to select the ''acceptable'' ones and, finally, to determine whether the statement can be accepted or not. Dung’s elegant account of abstract argumentation may have caused some to believe that defining an argumentation formalism is simply a matter of determining how arguments and their defeat relation can be constructed from a given knowledge base. Unfortunately, things are not that simple; many straightforward instantiations of Dung’s theory can lead to very unintuitive results, as is discussed in this paper. In order to avoid such anomalies, in this paper we are interested in defining some rules, called rationality postulates or axioms, that govern the well definition of an argumentation system. In particular, we define two important rationality postulates that any system should satisfy: the consistency and the closeness of the results returned by that system. We then provide a relatively easy way in which these quality postulates can be warranted by our argumentation system.